CN109783769B - Matrix decomposition method and device based on user project scoring - Google Patents
Matrix decomposition method and device based on user project scoring Download PDFInfo
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Abstract
The embodiment of the invention provides a matrix decomposition method and device based on user project scoring. The method comprises the following steps: constructing a mean square error loss function according to a user project rating matrix to be decomposed and a decomposition relation between a user factor matrix and a project factor matrix; carrying out iterative updating on the mean square error loss function for a plurality of times until the mean square error loss function after iterative updating meets a preset iterative condition, wherein the iteration step length corresponding to each variable element in different iterative processes dynamically changes along with the difference of the iterative times; and determining the values of the variable elements updated in the last iteration as the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix. The device is used for executing the method. The method and the device provided by the embodiment of the invention improve the accuracy of the decomposed user factor matrix and project factor matrix while improving the decomposition speed.
Description
Technical Field
The embodiment of the invention relates to the field of data processing, in particular to a matrix decomposition method and device based on user project scoring.
Background
The implicit factor matrix decomposition algorithm is to decompose a user item matrix (usually a high-dimensional sparse matrix, that is, many elements in the matrix are missing unknown) into two matrices, a user factor matrix and a item factor matrix, and assign values to the decomposed two matrices randomly at first, and then construct a loss function according to the value (that is, actual value) of the user item matrix and the corresponding value (that is, predicted value) of the product of the decomposed two matrices. In order to make the predicted values as close to the actual values as possible, it is desirable to make the loss function as small as possible.
At present, a random gradient descent method can be used to find the minimum value of the loss function, and the values of each element in the user factor matrix and the item factor matrix are optimized and updated by the random gradient descent method. When a certain condition is met so that iteration is terminated, the training is considered to be finished, and at the moment, the user factor matrix and the project factor matrix after the training is finished can be used for carrying out inner product to predict the vacant values in the corresponding user project matrix.
However, in the existing implicit factor matrix decomposition algorithm, since variable elements in the user factor matrix and the project factor matrix move along the direction of the negative gradient of the loss function at the same learning rate (step length), iteration can be performed for many times to approach the minimum value, and the decomposition speed is slow; or cause missing of the minimum value point, and accurate decomposition result cannot be obtained.
Disclosure of Invention
Aiming at the defects in the prior art, the embodiment of the invention provides a matrix decomposition method and device based on user item scoring, which improve the decomposition accuracy and the decomposition speed.
In one aspect, an embodiment of the present invention provides a matrix decomposition method based on user item scores, including:
constructing a mean square error loss function according to a user project rating matrix to be decomposed and a decomposition relation between a user factor matrix and a project factor matrix;
carrying out iterative updating on the mean square error loss function for a plurality of times in the following mode until the mean square error loss function after iterative updating meets the preset iterative condition:
aiming at each variable element in the user factor matrix and the project factor matrix, calculating an iteration step length corresponding to the variable element in the current iteration according to the current iteration times, wherein the calculated iteration step length is smaller than the iteration step length corresponding to the variable element in the previous iteration; according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function after the previous iteration update; judging whether the mean square error loss function after the iteration update meets a preset iteration condition, and if not, performing the next iteration; if yes, ending the iteration;
and determining the values of the variable elements updated in the last iteration as the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix.
In another aspect, an embodiment of the present invention provides a matrix decomposition device based on user item scores, including:
the construction module is used for constructing a mean square error loss function according to a user project score matrix to be decomposed and a decomposition relation between a user factor matrix and a project factor matrix;
the iteration module is used for carrying out iterative update on the mean square error loss function for a plurality of times in the following mode until the mean square error loss function after iterative update meets the preset iteration condition: aiming at each variable element in the user factor matrix and the project factor matrix, calculating an iteration step length corresponding to the variable element in the current iteration according to the current iteration times, wherein the calculated iteration step length is smaller than the iteration step length corresponding to the variable element in the previous iteration; according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function after the previous iteration update; judging whether the mean square error loss function after the iteration update meets a preset iteration condition, and if not, performing the next iteration; if so, ending the iteration and outputting the values of the variable elements updated in the iteration;
and the decomposition module is used for determining the value of each variable element output by the iteration module as the decomposition optimization value of each variable element in the user factor matrix and the project factor matrix.
In another aspect, an embodiment of the present invention provides an electronic device, including a processor, a memory, and a bus, where:
the processor and the memory complete mutual communication through a bus;
the processor may invoke a computer program in memory to perform the steps of the above-described method.
In yet another aspect, an embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored, where the computer program is used to implement the steps of the above method when executed by a processor.
According to the matrix decomposition method and device based on the user project score, a mean square error loss function is constructed according to a user project score matrix to be decomposed and a decomposition relation between a user factor matrix and a project factor matrix; iteratively updating the mean square error loss function for a plurality of times until the iteratively updated mean square error loss function meets a preset iteration condition, wherein the iteration step length corresponding to each variable element in different iteration processes dynamically changes along with different iteration times; and determining the values of the variable elements updated in the last iteration as decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix, so that the accuracy of the decomposed user factor matrix and the decomposed project factor matrix is improved while the decomposition speed is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 illustrates an exemplary flow diagram of a matrix decomposition method based on user item scoring according to one embodiment of the invention;
FIG. 2 is a schematic diagram illustrating an apparatus for matrix factorization based on user item scoring in accordance with one embodiment of the present invention;
fig. 3 shows a physical structure diagram of an electronic device according to an embodiment of the invention.
Detailed Description
The technical solutions of the present invention will be described below clearly and completely with reference to the accompanying drawings, and it is to be understood that the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As used in this application, the terms "module," "device," and the like are intended to encompass a computer-related entity, such as but not limited to hardware, firmware, a combination of hardware and software, or software in execution. For example, a module may be, but is not limited to: a process running on a processor, an object, an executable, a thread of execution, a program, and/or a computer. For example, an application running on a computing device and the computing device may both be a module. One or more modules may reside within a process and/or thread of execution and a module may be localized on one computer and/or distributed between two or more computers.
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
Referring to FIG. 1, an exemplary flow diagram of a matrix factorization method based on user item scoring in accordance with one embodiment of the present invention is shown.
As shown in fig. 1, the matrix decomposition method based on user item scores according to the embodiment of the present invention may include the following steps:
s110: and constructing a mean square error loss function according to the user item scoring matrix to be decomposed and the decomposition relation between the user factor matrix and the item factor matrix.
In the embodiment of the invention, the user item scoring matrix to be decomposed is constructed on the basis of a plurality of known user item scores; each variable element in the user factor matrix and the project factor matrix has an initial assignment. The decomposition relationship among the user item scoring matrix R, the user factor matrix U and the item factor matrix V is specifically as follows: r ≈ U T V。
In the embodiment of the invention, the user item score refers to the score of the user for the item. The items may be products or services, such as various APPs (applications) like music, video, reading, animation, games, etc.
In practical applications, for several known user item scores, a normalization process may be performed first, so that the normalized user item scores are between 0 and 1.
And then, constructing a user item score matrix to be decomposed based on the user item scores after the standardization processing. In consideration of the fact that the actual scores of all the items of the user cannot be obtained in practical application, the constructed user item score matrix is a sparse matrix, namely the user item score matrix comprises known user item scores and unknown user item scores.
And constructing two corresponding decomposition matrixes according to the user item scoring matrix: a user factor matrix and a project factor matrix; and carrying out initial assignment on variable elements in the user factor matrix and the project factor matrix.
Optionally, in the process of constructing the user factor matrix and the project factor matrix, a random assignment mode is adopted when performing initial assignment on each variable element in the user factor matrix and the project factor matrix.
In the embodiment of the present invention, the number of variable elements (which may be referred to as user factor variables in this embodiment) in the user factor matrix is a product of the number of hidden factors and the number of users; the user factor variable is used for representing the degree of association between the user and the hidden factor.
Accordingly, the number of variable elements (which may be referred to as item factor variables in this embodiment) in the item factor matrix is the product of the number of implicit factors and the number of items; the item factor variable is used to represent the degree of association between an item and a hidden factor.
Wherein, the number of the hidden factors can be set according to the filling rate of the constructed user item scoring matrix. In practical application, the higher the filling rate is, the smaller the number of hidden factors is; the lower the fill rate, the greater the number of hidden factors.
In the embodiment of the present invention, the mean square error loss function L may be constructed according to the following formula:
wherein N is the number of users, M is the number of projects, and the N is an integer greater than 1; r pq Scoring the qth item for the pth user; u shape p A vector composed of user factor variables representing the correlation degree between the p-th user and each hidden factor in the user factor matrix U; v q A vector composed of item factor variables representing the association degree between the qth item and each implicit factor in the item factor matrix V; λ is a preset regularization coefficient.
In practical applications, other formulas may also be used to construct the mean square error loss function L, such as:
wherein N is the number of users, M is the number of projects, and the N is an integer greater than 1; r pq Scoring the qth item for the pth user; u shape p A vector composed of user factor variables representing the correlation degree between the p-th user and each hidden factor in the user factor matrix U; v q A vector composed of item factor variables representing the association degree between the qth item and each implicit factor in the item factor matrix V; λ is a preset regularization coefficient, and p takes the value of [1]Q is [1, M ]]Is an integer of (1).
S120: carrying out iterative updating on the mean square error loss function for a plurality of times in the following mode until the mean square error loss function after iterative updating meets the preset iterative condition: aiming at each variable element in the user factor matrix and the project factor matrix, calculating the iteration step length corresponding to the variable element in the iteration according to the current iteration times; according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function after the previous iteration update; judging whether the mean square error loss function after the iteration update meets a preset iteration condition, and if not, performing the next iteration; if yes, the iteration is ended and step S130 is executed.
And calculating the iteration step length corresponding to the variable element in the current iteration, wherein the calculated iteration step length corresponding to the variable element in the previous iteration is smaller than the iteration step length corresponding to the variable element in the previous iteration.
In an embodiment of the present invention, the preset iteration condition includes any one of the following items:
the mean square error loss function reaches a minimum value, the mean square error loss function reaches a preset value, and the iteration times of the mean square error loss function are equal to a preset time threshold.
Wherein the preset function threshold is preset according to the minimum value. In practical application, a numerical value approaching a minimum value can be selected as a preset function threshold value for timely iteration according to different requirements of accuracy. For example, when the minimum value is 0, 0.001, 0.00001, or 0.00000001 may be selected as the preset function threshold.
In the embodiment of the invention, in one iteration process, the corresponding iteration step lengths of different variable elements in the current iteration process can be the same or different; for the same variable element, the iteration step corresponding to the variable element is dynamically changed, and the iteration steps corresponding to the variable element in different iteration processes are different. And with the continuous increase of the iteration times, the iteration step length corresponding to the variable element is continuously reduced.
Wherein, the variable element is a variable element in the user factor matrix or a variable element in the project factor matrix.
In the embodiment of the invention, in each iteration process, after the updated mean square error loss function is obtained, the gradient value of the mean square error loss function on each variable element can be calculated and stored.
In this way, in the subsequent process of performing the (I + 1) th iteration, for each user factor variable in the user factor matrix, I gradient values of the mean square error loss function on the user factor variable after the previous I iterations are updated can be obtained; and determining the iteration step length corresponding to the user factor variable in the I +1 th iteration according to the current iteration times I, the obtained I gradient values and a preset initial iteration step length.
For each item factor variable in the item factor matrix, acquiring I gradient values of the mean square error loss function on the item factor variable after the previous I iterations are updated; and determining the iteration step length corresponding to the item factor variable in the I +1 th iteration according to the current iteration times I, the obtained I gradient values and a preset initial iteration step length.
Then, according to the iteration step length corresponding to each user factor variable and the iteration step length corresponding to each project factor variable, updating variable elements of the mean square error loss function after the previous iteration updating; and if the mean square error loss function updated by the iteration does not meet the preset iteration condition, performing the next iteration. If the updated mean square error loss function of the iteration satisfies the preset iteration condition, the iteration is ended, and step S130 is executed.
S130: and determining the values of the variable elements updated in the last iteration as the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix.
In the embodiment of the invention, under the condition that the updated mean square error loss function of the current iteration meets the preset iteration condition, the current iteration is the last iteration of the mean square error loss function. Obtaining values of each user factor variable and each project factor variable updated in the last iteration, and taking the obtained values of each user factor variable as decomposition optimization values of each user factor variable of the user factor matrix; and meanwhile, the acquired value of each item factor variable is used as the decomposition optimization value of each item factor variable of the item factor matrix.
Under the condition that each variable element in the user factor matrix and the project factor matrix takes a decomposition optimization value, a mean square error loss function constructed based on the user project scoring matrix, the user factor matrix and the project factor matrix meets a preset iteration condition, for example, a minimum value is reached. Therefore, the predicted score of the user for the project obtained by inner product calculation of the user factor matrix and the project factor matrix is closer to the actual score of the user for the project, and the decomposition result is more accurate.
According to the matrix decomposition method based on the user project score, provided by the embodiment of the invention, a mean square error loss function is constructed according to a user project score matrix to be decomposed and a decomposition relation between a user factor matrix and a project factor matrix; carrying out iterative updating on the mean square error loss function for a plurality of times until the mean square error loss function after iterative updating meets a preset iterative condition, wherein the iteration step length corresponding to each variable element in different iterative processes dynamically changes along with the difference of the iterative times; and determining the values of the variable elements updated in the last iteration as decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix, so that the accuracy of the decomposed user factor matrix and the decomposed project factor matrix is improved while the decomposition speed is improved.
On the basis of the foregoing embodiment, in the matrix decomposition method based on user item scores according to another embodiment of the present invention, the calculating, for each variable element in the user factor matrix and the item factor matrix, an iteration step corresponding to the variable element in the current iteration according to the current iteration number includes:
for each variable element w, calculating the iteration step length gamma corresponding to the variable element w in the I +1 th iteration according to the following formula w ：
Wherein I represents the current iteration times, and the value of I is an integer greater than or equal to 0; g wi Representing the gradient value of the mean square error loss function on the variable element w after the ith iteration update, wherein the value of i is [0]An integer of (a); gamma denotes a preset initial iteration step, g w0 ＝1。
Specifically, the number of iterations that have been performed before the current iteration, that is, the current number of iterations I, may be determined first; and acquiring gradient values of the I iteration updated mean square error loss functions on each variable element before the current iteration.
Then, according to the formula
Determining the iteration (i.e. theIteration step corresponding to the variable element in the I +1 th iteration).
In practical application, in the process of performing 1 st iteration, the current number of iterations is 0, and therefore, the iteration step lengths corresponding to the variable elements in the 1 st iteration are the same and are all the preset initial iteration step lengths γ.
In the embodiment of the invention, in the process of I +1 iteration, for each user factor variable in a user factor matrix, I gradient values of a mean square error loss function on the user factor variable after the previous I iterations are updated can be obtained; according to the current iteration times I, the obtained I gradient values and a preset initial iteration step length, a formula is utilized
And calculating the iteration step length corresponding to the user factor variable in the I +1 th iteration.
For each item factor variable in the item factor matrix, I gradient values of the mean square error loss function on the item factor variable after I times of iteration updating can be obtained; according to the current iteration times I, the obtained I gradient values and a preset initial iteration step length, a formula is utilized
And determining the iteration step size corresponding to the item factor variable in the I +1 th iteration.
Therefore, in the iteration process, the iteration step length of the variable elements is reduced along with the increase of the iteration times, so that the process from coarse tuning to fine tuning of the mean square error loss function is realized, and the mean square error loss function continuously approaches to a minimum value point. Further, since the mean square error loss function has different gradient values on different variable elements, the respective iteration step lengths corresponding to different variable elements are also different.
Other steps of the embodiment of the present invention are similar to those of the previous embodiment, and are not repeated herein.
According to the matrix decomposition method based on user project grading, provided by the embodiment of the invention, the iteration step length of dynamic change is introduced, so that the mean square error loss function can quickly and accurately approach to a minimum value through the process from coarse adjustment to fine adjustment, and a decomposition result with high accuracy is quickly obtained.
On the basis of the foregoing embodiment, in the matrix decomposition method based on user item scores provided in another embodiment of the present invention, the updating variable elements of the mean square error loss function after the previous iteration update according to the respective iteration step lengths corresponding to the variable elements includes:
for each variable element, randomly selecting one or more scores associated with the variable element from the known user item scores in the user item score matrix as a sample user item score corresponding to the variable element in the iteration;
for each variable element, calculating a negative gradient value of a mean square error loss function corresponding to the variable element after the previous iteration on the variable element according to the corresponding sample user item score of the variable element in the current iteration and the updated variable element value in the previous iteration;
and updating the variable elements of the mean square error loss function updated by the previous iteration according to the iteration step length corresponding to each variable element and the negative gradient value of the mean square error loss function updated by the previous iteration on each variable element.
In particular, for the user factor variable U in the user factor matrix pk Randomly selecting one or more of the sum and the U from the known user item scores in the user item score matrix pk The associated score is U pk The corresponding sample user item scores in this iteration.
For each item factor variable V in the item factor matrix kq Randomly selecting one or more of the sum V and the score of the user item from the known user item scores in the user item score matrix kq The associated score is taken as V kq The corresponding sample user item scores in this iteration.
Wherein, U pk And a variable element which represents the relevance between the p-th user and the k-th hidden factor in the user factor matrix U. V kq The expression item factor in the matrix VVariable elements of the degree of association between the q items and the kth hidden factor. p is [1, N ]]Q is [1, M ]]K is [1, K ]]N is the number of users, and the value is an integer greater than 1; m is the number of items, and the value is an integer larger than 1; k is the number of hidden factors and takes the value of an integer larger than 1.
In practical application, for the p-th user, the user has an actual score for a plurality of items in the M items, that is, a known user item score; for the qth project, there are several users in the N users who have actual scores for the project, i.e., known user project scores. Therefore, in the embodiment of the present invention, the actual scores of the p-th user on one or more items may be randomly selected as U pk Scoring corresponding sample user items in the iteration; randomly selecting the actual scores of the q-th project of one or more users as a variable V kq The corresponding sample user item scores in this iteration.
And then, for each variable element, calculating a negative gradient value of the mean square error loss function corresponding to the previous iteration on the variable element according to the sample user item score corresponding to the variable element in the current iteration and the values of the variable elements updated in the previous iteration.
And then, updating the variable elements of the mean square error loss function updated by the previous iteration according to the iteration step length corresponding to each variable element and the negative gradient value of the mean square error loss function updated by the previous iteration on each variable element. Specifically, for each variable element w, the updated variable element w' may be determined according to the following formula:
wherein the content of the first and second substances,
a negative gradient value, gamma, of the mean square error loss function L on the variable element w updated for the previous iteration w And the iteration step length corresponding to the variable element w in the iteration is obtained.
And finally, substituting each updated variable element into the mean square error loss function updated in the previous iteration to obtain the mean square error loss function updated in the current iteration.
In the embodiment of the present invention, the calculation of the negative gradient value and the variable update may adopt technical means commonly used by those skilled in the art, and are not described herein again.
Other steps of the embodiment of the present invention are similar to those of the previous embodiment, and are not described again in the embodiment of the present invention.
According to the matrix decomposition method based on the user item scores, the sample user item scores corresponding to all variable elements in the iteration process are randomly selected from the known user item scores, and the negative gradient value of the mean square error loss function corresponding to the variable elements after the previous iteration is calculated based on the selected sample user item scores; and then, according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function updated in the previous iteration, and enabling the variable element to move along the negative gradient direction of the mean square error loss function until the variable element moves to a minimum point.
On the basis of the above embodiment, in a matrix decomposition method based on user item scores provided by another embodiment of the present invention, the method further includes:
calculating the prediction scores of the user to the projects according to the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix;
calculating an error between the known user item score and the calculated predicted score; wherein the error comprises: mean square error and/or mean absolute value error;
if the error exceeds a set error threshold, carrying out optimization adjustment on at least one of the following according to the error:
the mean square error loss function, the total number of variable elements in the user factor matrix and the project factor matrix, and the initial iteration step.
After the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix are determined through step S130, the predicted score of the user on the project obtained by performing inner product calculation on the user factor matrix and the project factor matrix is closer to the actual score of the user on the project, and the decomposition result is more accurate.
In order to further guarantee the decomposition accuracy, in the embodiment of the present invention, the accuracy of the decomposition result may be checked according to the known user item score. Specifically, the values can be optimized according to the decomposition of each variable element in the user factor matrix and the project factor matrix to calculate the prediction scores of different users for different projects.
For example, the predictive score for the qth item by the pth user may be given by the vector U p And vector V q The inner product of (a) is calculated.
Wherein, U p And forming a vector by user factor variables representing the association degree between the p-th user and each hidden factor in the user factor matrix U. V q And a vector formed by each item factor variable representing the association degree between the q-th item and each hidden factor in the item factor matrix V.
Then, calculating the mean square error or the average absolute value error between the actual rating of the user to the project and the prediction rating of the user to the project; the calculated mean square error or mean absolute value error is compared with a preset error threshold. Wherein the error threshold is set according to the actual accuracy requirement.
If the calculated error exceeds the error threshold, the decomposition result does not meet the actual accuracy requirement, and further optimization is needed. In the embodiment of the present invention, the optimization and adjustment may be performed for at least one of the following according to the error:
the total number of variable elements in the mean square error loss function, the user factor matrix and the project factor matrix, and the initial iteration step length.
In practical application, the structure of the mean square error loss function can be adjusted, for example, the regularization coefficient in the mean square error loss function is adjusted; or adjusting the number of the hidden factors so as to adjust the total number of variable elements in the user factor matrix and the project factor matrix; alternatively, the initial iteration step size may be decreased.
Optionally, the preset iteration condition is that the preset number threshold may be increased when the number of iterations of the mean square error loss function is equal to the preset number threshold; the preset iteration condition is that the preset function threshold value can be reduced under the condition that the mean square error loss function reaches the preset function threshold value.
In this way, after optimization and adjustment, matrix decomposition is carried out on the user item score matrix to be decomposed based on the user item scores again until a decomposition result meeting the actual accuracy requirement is obtained.
Other steps of the embodiment of the present invention are similar to those of the previous embodiment, and are not described again in the embodiment of the present invention.
According to the matrix decomposition method based on the user project scores, the decomposition results are verified through the known user project scores, and the accuracy of the decomposition results is improved.
On the basis of the above embodiment, in a matrix decomposition method based on user item scores provided by another embodiment of the present invention, the method further includes:
determining the prediction scores of the user for each item according to the decomposition optimization values of each variable element in the user factor matrix and the project factor matrix;
and selecting a plurality of items as items to be recommended according to the sequence of the prediction scores of the items by the user.
Specifically, after the decomposed decomposition optimization values of the user factor matrix and the variable elements in the item factor matrix are determined in step S130, for any user, the prediction scores of the user for each item may be calculated according to the decomposition optimization values of the user factor variables associated with the user in the user factor matrix and the decomposition optimization values of the item factor variables in the item factor matrix.
And then, sequencing the prediction scores of the items by the user, and selecting a plurality of items with high prediction scores as items to be recommended so as to recommend the items to be recommended to the user.
Other steps of the embodiment of the present invention are similar to those of the previous embodiment, and are not described again in the embodiment of the present invention.
The matrix decomposition method based on the user project score provided by the embodiment of the invention can be used for recommending projects according to the decomposition result with high accuracy, so that the user experience can be improved.
On the basis of the above embodiments, another embodiment of the present invention provides a matrix decomposition device based on user item scores.
Referring to fig. 2, a schematic structural diagram of a matrix factorization apparatus based on user item scoring according to an embodiment of the present invention is shown.
As shown in fig. 2, an apparatus 200 for matrix decomposition based on user item scores according to an embodiment of the present invention may include: a construction module 201, an iteration module 202 and a decomposition module 203.
The construction module 201 is configured to construct a mean square error loss function according to a user item score matrix to be decomposed, and a decomposition relationship between a user factor matrix and a item factor matrix.
The user item scoring matrix to be decomposed is constructed based on a plurality of known user item scores, and each variable element in the user factor matrix and the item factor matrix has an initial assignment.
The iteration module 202 is configured to perform iterative update on the mean square error loss function for several times in the following manner until the iteratively updated mean square error loss function meets a preset iteration condition: aiming at each variable element in the user factor matrix and the project factor matrix, calculating an iteration step length corresponding to the variable element in the current iteration according to the current iteration times, wherein the calculated iteration step length is smaller than the iteration step length corresponding to the variable element in the previous iteration; according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function after the previous iteration update; judging whether the mean square error loss function after the iteration update meets a preset iteration condition, and if not, performing the next iteration; if so, ending the iteration and outputting the values of the variable elements updated in the iteration.
The decomposition module 203 is configured to determine the value of each variable element output by the iteration module 202 as a decomposition optimized value of each variable element in the user factor matrix and the project factor matrix.
Optionally, the preset iteration condition includes any one of:
the mean square error loss function reaches a minimum value, the mean square error loss function reaches a preset function threshold value, and the iteration times of the mean square error loss function are equal to a preset time threshold value;
wherein the preset function threshold is preset according to the minimum value.
Optionally, the iteration module 202 is configured to calculate, for each variable element w, an iteration step γ corresponding to the variable element w in the I +1 th iteration according to the following formula w ：
Wherein I represents the current iteration times, and the value of I is an integer greater than or equal to 0; g wi Representing the gradient value of the mean square error loss function on the variable element w after the ith iteration update, wherein the value of i is [0]An integer of (d); gamma denotes a preset initial iteration step, g w0 ＝1。
Optionally, the iteration module 202 is configured to, for each variable element, randomly select one or more scores associated with the variable element from known user item scores in the user item score matrix as a sample user item score corresponding to the variable element in the current iteration; for each variable element, calculating a negative gradient value of a mean square error loss function corresponding to the variable element after the previous iteration according to the corresponding sample user item score of the variable element in the current iteration and the updated variable element value in the previous iteration; and updating the variable elements of the mean square error loss function updated by the previous iteration according to the iteration step length corresponding to each variable element and the negative gradient value of the mean square error loss function updated by the previous iteration on each variable element.
Optionally, the iteration module 202 is configured to determine, for each variable element w, an updated variable element w' according to the following formula:
wherein the content of the first and second substances,
a negative gradient value, gamma, of the mean square error loss function L on the variable element w updated for the previous iteration w The iteration step length corresponding to the variable element w in the iteration is obtained; and substituting the updated variable elements into the mean square error loss function updated in the previous iteration to obtain the mean square error loss function updated in the current iteration.
Optionally, the apparatus 200 for decomposing a matrix based on user item scores may further include: and an optimization module.
The optimization module is used for calculating the prediction scores of the users to the projects according to the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix; calculating an error between the known user item score and the calculated predicted score; wherein the error comprises: mean square error and/or mean absolute value error; if the error exceeds a set error threshold, carrying out optimization adjustment on at least one of the following according to the error: the mean square error loss function, the total number of variable elements in the user factor matrix and the project factor matrix, and the initial iteration step.
Optionally, the apparatus 200 for matrix decomposition based on user item scores may further include: and a recommendation module.
The recommendation module is used for determining the prediction scores of the user for each item according to the decomposition optimization values of the variable elements in the user factor matrix and the item factor matrix; and selecting a plurality of items as the items to be recommended according to the sequence of the prediction scores of the items by the user.
According to the matrix decomposition device based on the user project score, provided by the embodiment of the invention, a mean square error loss function is constructed according to the decomposition relation among a user project score matrix to be decomposed, a user factor matrix and a project factor matrix; carrying out iterative updating on the mean square error loss function for a plurality of times until the mean square error loss function after iterative updating meets a preset iterative condition, wherein the iteration step length corresponding to each variable element in different iterative processes dynamically changes along with the difference of the iterative times; and determining the values of the variable elements updated in the last iteration as decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix, so that the decomposition speed is increased, and the accuracy of the decomposed user factor matrix and the decomposed project factor matrix is improved.
The embodiment of the matrix decomposition device based on user item scores provided by the present invention may be specifically configured to execute the processing flows of the above method embodiments, and the functions thereof are not described herein again, and reference may be made to the detailed description of the above method embodiments.
Referring to fig. 3, a physical structure diagram of an electronic device according to an embodiment of the invention is shown. As shown in fig. 3, the electronic device 300 may include: a processor (processor) 301, a memory (memory) 302 and a bus 303, wherein the processor 301 and the memory 302 communicate with each other through the bus 303. The processor 301 may call the computer program in the memory 302 to execute the methods provided by the method embodiments described above, for example, including:
constructing a mean square error loss function according to a user project rating matrix to be decomposed and a decomposition relation between a user factor matrix and a project factor matrix;
carrying out iterative updating on the mean square error loss function for a plurality of times in the following mode until the mean square error loss function after iterative updating meets the preset iterative condition:
aiming at each variable element in the user factor matrix and the project factor matrix, calculating an iteration step length corresponding to the variable element in the current iteration according to the current iteration times, wherein the calculated iteration step length is smaller than the iteration step length corresponding to the variable element in the previous iteration; according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function after the previous iteration updating; judging whether the mean square error loss function after the iteration update meets a preset iteration condition, and if not, performing the next iteration; if yes, ending the iteration;
and determining the values of the variable elements updated in the last iteration as the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix.
In another embodiment, the preset iteration condition includes any one of the following items:
the mean square error loss function reaches a minimum value, the mean square error loss function reaches a preset function threshold value, and the iteration times of the mean square error loss function are equal to a preset time threshold value;
wherein the preset function threshold is preset according to the minimum value.
In another embodiment, the processor 301, when executing the computer program, implements the following method:
the calculating, for each variable element in the user factor matrix and the project factor matrix, an iteration step corresponding to the variable element in the current iteration according to the current iteration number includes:
for each variable element w, calculating an iteration step length gamma corresponding to the variable element w in the I +1 th iteration according to the following formula w ：
Wherein I represents the current iteration times, and the value of I is an integer greater than or equal to 0; g wi Representing the gradient value of the mean square error loss function on the variable element w after the ith iteration update, wherein the value of i is [0]An integer of (a); gamma denotes a preset initial iteration step, g w0 ＝1。
In another embodiment, the processor 301, when executing the computer program, implements the following method:
the updating the variable elements of the mean square error loss function after the previous iteration updating according to the iteration step length corresponding to each variable element comprises the following steps:
for each variable element, randomly selecting one or more scores associated with the variable element from the known user item scores in the user item score matrix as a sample user item score corresponding to the variable element in the iteration;
for each variable element, calculating a negative gradient value of a mean square error loss function corresponding to the variable element after the previous iteration according to the corresponding sample user item score of the variable element in the current iteration and the updated variable element value in the previous iteration;
and updating the variable elements of the mean square error loss function updated by the previous iteration according to the iteration step length corresponding to each variable element and the negative gradient value of the mean square error loss function updated by the previous iteration on each variable element.
In another embodiment, the processor 301, when executing the computer program, implements the following method:
the updating of the variable element of the mean square error loss function after the previous iteration update comprises:
for each variable element w, the updated variable element w' is determined according to the following formula:
wherein the content of the first and second substances,
a negative gradient value, gamma, of the mean square error loss function L on the variable element w updated for the previous iteration w The iteration step length corresponding to the variable element w in the iteration is obtained;
and substituting each updated variable element into the mean square error loss function updated in the previous iteration to obtain the mean square error loss function updated in the current iteration.
In another embodiment, the processor 301, when executing the computer program, implements the following method:
calculating the prediction scores of the user to the projects according to the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix;
calculating an error between the known user item score and the calculated predicted score; wherein the error comprises: mean square error and/or mean absolute value error;
if the error exceeds a set error threshold, carrying out optimization adjustment on at least one of the following according to the error:
the mean square error loss function, the total number of variable elements in the user factor matrix and the project factor matrix, and the initial iteration step.
In another embodiment, the processor 301, when executing the computer program, implements the following method:
determining the prediction scores of the user for each item according to the decomposition optimization values of each variable element in the user factor matrix and the project factor matrix;
and selecting a plurality of items as items to be recommended according to the sequence of the prediction scores of the items by the user.
The electronic equipment provided by the embodiment of the invention at least has the following technical effects: constructing a mean square error loss function according to a user project rating matrix to be decomposed and a decomposition relation between a user factor matrix and a project factor matrix; carrying out iterative updating on the mean square error loss function for a plurality of times until the mean square error loss function after iterative updating meets a preset iterative condition, wherein the iteration step length corresponding to each variable element in different iterative processes dynamically changes along with the difference of the iterative times; and determining the values of the variable elements updated in the last iteration as decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix, so that the decomposition speed is increased, and the accuracy of the decomposed user factor matrix and the decomposed project factor matrix is improved.
An embodiment of the present invention discloses a computer program product, which includes a computer program stored on a non-transitory computer readable storage medium, the computer program including program instructions, when the program instructions are executed by a computer, the computer can execute the methods provided by the above method embodiments, for example, the method includes:
constructing a mean square error loss function according to a user project rating matrix to be decomposed and a decomposition relation between a user factor matrix and a project factor matrix; carrying out iterative updating on the mean square error loss function for a plurality of times in the following mode until the mean square error loss function after iterative updating meets the preset iterative condition: aiming at each variable element in the user factor matrix and the project factor matrix, calculating an iteration step length corresponding to the variable element in the current iteration according to the current iteration times, wherein the calculated iteration step length is smaller than the iteration step length corresponding to the variable element in the previous iteration; according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function after the previous iteration updating; judging whether the mean square error loss function after the iteration update meets a preset iteration condition, and if not, performing the next iteration; if yes, ending the iteration; and determining the values of the variable elements updated in the last iteration as the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix.
An embodiment of the present invention provides a non-transitory computer-readable storage medium, where the non-transitory computer-readable storage medium stores a computer program, where the computer program causes the computer to execute the method provided by the foregoing method embodiments, for example, the method includes:
constructing a mean square error loss function according to a user project rating matrix to be decomposed and a decomposition relation between a user factor matrix and a project factor matrix; iteratively updating the mean square error loss function for a plurality of times in the following way until the iteratively updated mean square error loss function meets the preset iteration condition: aiming at each variable element in the user factor matrix and the project factor matrix, calculating an iteration step length corresponding to the variable element in the current iteration according to the current iteration times, wherein the calculated iteration step length is smaller than the iteration step length corresponding to the variable element in the previous iteration; according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function after the previous iteration updating; judging whether the mean square error loss function after the iteration update meets a preset iteration condition, and if not, performing the next iteration; if yes, ending the iteration; and determining the values of the variable elements updated in the last iteration as the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix.
In addition, the logic instructions in the memory may be implemented in the form of software functional units and may be stored in a computer readable storage medium when sold or used as a stand-alone product. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk, and various media capable of storing program codes.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one position, or may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods according to the various embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (9)
1. A matrix decomposition method based on user item scoring is characterized by comprising the following steps:
constructing a mean square error loss function according to a user item score matrix to be decomposed and a decomposition relation between a user factor matrix and a item factor matrix, wherein the user items comprise a music application APP, a video APP, a reading APP, a cartoon APP and a game APP;
carrying out iterative updating on the mean square error loss function for a plurality of times in the following mode until the mean square error loss function after iterative updating meets the preset iterative condition:
aiming at each variable element in the user factor matrix and the project factor matrix, calculating an iteration step length corresponding to the variable element in the current iteration according to the current iteration times, wherein the calculated iteration step length is smaller than the iteration step length corresponding to the variable element in the previous iteration; according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function after the previous iteration update; judging whether the mean square error loss function after the iteration update meets a preset iteration condition, and if not, performing the next iteration; if yes, ending the iteration;
wherein, the calculating, for each variable element in the user factor matrix and the project factor matrix, an iteration step corresponding to the variable element in the current iteration according to the current iteration number includes:
for each variable element w, calculating the iteration step length gamma corresponding to the variable element w in the I +1 th iteration according to the following formula w ：
Wherein I represents the current iteration times, and the value of I is an integer greater than or equal to 0; g is a radical of formula wi Representing the gradient value of the mean square error loss function on the variable element w after the ith iteration update, wherein the value of i is [0]An integer of (d); gamma denotes a preset initial iteration step, g w0 ＝1；
And determining the values of the variable elements updated in the last iteration as the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix.
2. The method according to claim 1, wherein the preset iteration condition comprises any one of:
the mean square error loss function reaches a minimum value, the mean square error loss function reaches a preset function threshold value, and the iteration number of the mean square error loss function is equal to a preset number threshold value;
wherein the preset function threshold is preset according to the minimum value.
3. The method according to claim 1, wherein the updating the variable elements of the mean square error loss function updated in the previous iteration according to the respective iteration step lengths corresponding to the variable elements comprises:
for each variable element, randomly selecting one or more scores associated with the variable element from the known user item scores in the user item score matrix as a sample user item score corresponding to the variable element in the iteration;
for each variable element, calculating a negative gradient value of a mean square error loss function corresponding to the variable element after the previous iteration according to the corresponding sample user item score of the variable element in the current iteration and the updated variable element value in the previous iteration;
and updating the variable elements of the mean square error loss function updated by the previous iteration according to the iteration step length corresponding to each variable element and the negative gradient value of the mean square error loss function updated by the previous iteration on each variable element.
4. The method of claim 3, wherein the updating the mean square error loss function updated from the previous iteration with a variable element update comprises:
for each variable element w, the updated variable element w' is determined according to the following formula:
wherein-
A negative gradient value, gamma, of the mean square error loss function L on the variable element w updated for the previous iteration w The iteration step length corresponding to the variable element w in the iteration is obtained;
and substituting each updated variable element into the mean square error loss function updated in the previous iteration to obtain the mean square error loss function updated in the current iteration.
5. The method of any of claims 1-4, further comprising:
calculating the prediction scores of the user to the projects according to the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix;
calculating an error between the known user item score and the calculated predicted score; wherein the error comprises: mean square error and/or mean absolute value error;
if the error exceeds a set error threshold, carrying out optimization adjustment on at least one of the following according to the error:
the mean square error loss function, the total number of variable elements in the user factor matrix and the project factor matrix, and the initial iteration step length.
6. The method according to any one of claims 1-4, further comprising:
determining the prediction scores of the user for each item according to the decomposition optimization values of the variable elements in the user factor matrix and the project factor matrix;
and selecting a plurality of items as the items to be recommended according to the sequence of the prediction scores of the items by the user.
7. An apparatus for matrix factorization based on user project scoring, comprising:
the system comprises a construction module, a storage module and a processing module, wherein the construction module is used for constructing a mean square error loss function according to a user project score matrix to be decomposed, and a decomposition relation between a user factor matrix and a project factor matrix, wherein the user project comprises a music application APP, a video APP, a reading APP, a cartoon APP and a game APP;
the iteration module is used for carrying out a plurality of times of iterative updating on the mean square error loss function in the following mode until the mean square error loss function after iterative updating meets the preset iteration condition: aiming at each variable element in the user factor matrix and the project factor matrix, calculating an iteration step length corresponding to the variable element in the current iteration according to the current iteration times, wherein the calculated iteration step length is smaller than the iteration step length corresponding to the variable element in the previous iteration; according to the iteration step length corresponding to each variable element, updating the variable element of the mean square error loss function after the previous iteration updating; judging whether the mean square error loss function after the iteration update meets a preset iteration condition, and if not, performing the next iteration; if so, ending the iteration and outputting the values of the variable elements updated in the iteration;
the iteration module is further to:
for each variable element w, calculating an iteration step length gamma corresponding to the variable element w in the I +1 th iteration according to the following formula w ：
Wherein I represents the current iteration times, and the value of I is an integer greater than or equal to 0; g wi Representing the gradient value of the mean square error loss function on the variable element w after the ith iteration update, wherein the value of i is [0]An integer of (d); gamma denotes a preset initial iteration step, g w0 ＝1；
And the decomposition module is used for determining the value of each variable element output by the iteration module as the decomposition optimization value of each variable element in the user factor matrix and the project factor matrix.
8. An electronic device comprising a processor, a memory, and a bus, wherein:
the processor and the memory complete mutual communication through a bus;
the processor may invoke a computer program in memory to perform the steps of the method of any of claims 1-6.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 6.
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